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7.2 The Nature of Matter It is probably fair to say that at the end of the nineteenth century, physicists were feeling rather smug. Theories could explain phenomena as diverse as the motions of the planets and the dispersion of visible light by a prism. Rumor has it that students were being discouraged from pursuing physics as a career because it was felt that all the major problems had been solved, or at least described in terms of the current physical theories.

At the end of the nineteenth century, the idea prevailed that matter and energy were distinct. Matter was thought to consist of particles, whereas energy in the form of light (electromagnetic radiation) was described as a wave. Particles were things that had mass and whose position in space could be specified. Waves were described as massless and delocalized; that is, their position in space could not be specified. It also was assumed that there was no intermingling of matter and light. Everything known before 1900 seemed to fit neatly into this view.

At the beginning of the twentieth century, however, certain experimental results suggested that this picture was incorrect. The first important advance came in 1900 from the German physicist Max Planck (1858–1947). Studying the radiation profiles emitted by solid bodies heated to incandescence, Planck found that the results could not be explained in terms of the physics of his day, which held that matter could absorb or emit any quantity of energy. Planck could account for these observations only by postulating that energy can be gained or lost only in whole-number multiples of the quantity , where is a constant called Planck’s constant (the constant relating the change in energy for a system to the frequency of the electromagnetic radiation absorbed or emitted; equal to

.) , determined by experiment to have the value . That is, the change in energy for a system, , can be represented by the equation

where is an integer , is Planck’s constant, and is the frequency of the electromagnetic radiation absorbed or emitted.

Planck’s result was a real surprise. It had always been assumed that the energy of matter was continuous, which meant that the transfer of any quantity of energy was possible. Now it seemed clear that energy is in fact quantized (the concept that energy can occur only in discrete units called quanta.) and can occur only in discrete units of size . Each of these small “packets” of energy is called a quantum. A system can transfer energy only in whole quanta. Thus energy seems to have particulate properties.

Interactive Example 7.2

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The Energy of a Photon

The blue color in fireworks is often achieved by heating copper chloride to about . Then the compound emits blue light having a wavelength of nm. What is the increment of energy (the quantum) that is emitted at nm by

Solution

The quantum of energy can be calculated from the equation

The frequency for this case can be calculated as follows:

A sample of emitting light at nm can lose energy only in increments of J, the size of the quantum in this case.

See Exercises 7.47 and 7.48

The next important development in the knowledge of atomic structure came when Albert Einstein (Fig. 7.3) proposed that electromagnetic radiation is itself quantized. Einstein suggested that electromagnetic radiation can be viewed as a stream of “particles” called photons (a quantum of electromagnetic radiation.) . The energy of each photon is given by the expression

where is Planck’s constant, is the frequency of the radiation, and is the wavelength of the radiation.

Figure 7.3

Albert Einstein (1879–1955) was born in Germany. Nothing in his early development suggested genius; even at the age of 9 he did not speak clearly, and his parents feared that he might be handicapped. When asked what profession Einstein should follow, his school principal replied, “It doesn’t matter; he’ll never make a success of anything.” When he was 10, Einstein entered the Luitpold Gymnasium (high school), which was typical of German schools of that time in being harshly disciplinarian. There he developed a deep suspicion of authority and

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a skepticism that encouraged him to question and doubt—valuable qualities in a scientist. In 1905, while a patent clerk in Switzerland, Einstein published a paper explaining the photoelectric effect via the quantum theory. For this revolutionary thinking, he received a Nobel Prize in 1921. Highly regarded by this time, he worked in Germany until 1933, when Hitler’s persecution of the Jews forced him to come to the United States. He worked at the Institute for Advanced Studies in Princeton, New Jersey, until his death in 1955.

Einstein was undoubtedly the greatest physicist of our age. Even if someone else had derived the theory of relativity, his other work would have ensured his ranking as the second greatest physicist of his time. Our concepts of space and time were radically changed by ideas he first proposed when he was 26 years old. From then until the end of his life, he attempted unsuccessfully to find a single unifying theory that would explain all physical events.

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